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An airplane flies 200 km due west from city A to city B and then 280 km in the direction of 30.5┬░ north of west from city B to city C.
(a) In straight-line distance, how far is city C from city A?
in km?

(b) Relative to city A, in what direction is city C?
how many┬░ north of west

  • physics -

    (1) Add the vector going from A to B and the vector going from B to C. The length of the resultant vector will tell you the distance from A to C.
    (2) The direction of the resultant vector of step 1 is what you are looking for. The angle (measured north from west) is arctan (Change in y)/(-Change in x)
    = arctan (280 sin 30.5)/(200 + 280 cos 30.5) = arctan [142.1/(200 +241.2)]
    17.8 degrees

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